Non-linear wave equations coupled to generalized massive-massless Vlasov equations
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Consider Einstein’s field equations where the matter model consists oftwo momentum distribution functions. Let the first momentum distribution function represent massive matter, for instance galactic dust, and let the second represent massless matter, for instance radiation. Furthermore,let us require that each of the momentum distribution functions shall satisfy the Vlasov equation. This means that the momentum distribution functions represent collisionless matter. If Einstein’s field equations withsuch a matter model is expressed in coordinates and if certain gauges arefixed we get a system of integro-partial differential equations we shall call non-linear wave equations coupled to generalized massive-massless Vlasovequations. We prove that the initial value problem associated to this kindof equations has a unique local solution. Moreover, we prove a continuation criterion for the solution.
Einstein's field equations, Vlasov equations
Geometry Mathematical Analysis
IdentifiersURN: urn:nbn:se:kth:diva-93786OAI: oai:DiVA.org:kth-93786DiVA: diva2:523839